The CD and NND distributions of an MCP were first characterized for the 2-D case in [1]} (and for Thomas cluster process, another special case of PCP, in [2]}). However, the expressions involve multiple integrals and are thus unwieldy. A simpler expression for the CD for a 2-D MCP was derived in [3]}. In general, there are two main approaches to these derivations. The first one uses the probability generating functional (PGFL) of a PCP [4]} and is also the approach taken in [1]}.  For a detailed discussion on MCP, readers are advised to refer [1]} and references therein. The second approach is to condition on the parent PPP of the PCP and then use the PGFL
of a PPP. While this general approach has been used recently for the coverage analysis of cellular networks in [7]}, [8]}, we will demonstrate in this letter that a similar approach can also be leveraged to derive remarkably simple expressions for the CD and NND distributions of an \(n\) -D MCP. We also develop novel closed-form upper and lower bounds on these distributions in order to provide further insights. While the construction of these bounds is seemingly straightforward (involves developing simple bounds on the intersection of \(n\) -D balls), the resulting bounds are remarkably tight, which is also verified using numerical comparisons.
